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Approximating discrete valuation rings by regular local rings


Authors: William Heinzer, Christel Rotthaus and Sylvia Wiegand
Journal: Proc. Amer. Math. Soc. 129 (2001), 37-43
MSC (1991): Primary 13F30, 13H05; Secondary 13E05, 13G05, 13J05, 13J15
DOI: https://doi.org/10.1090/S0002-9939-00-05492-7
Published electronically: July 27, 2000
MathSciNet review: 1694346
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $k$ be a field of characteristic zero and let $(V,\mathbf{n})$ be a discrete rank-one valuation domain containing $k$ with $V/\mathbf{n}= k$. Assume that the fraction field $L$ of $V$has finite transcendence degree $s$ over $k$. For every positive integer $d \le s$, we prove that $V$ can be realized as a directed union of regular local $k$-subalgebras of $V$ of dimension $d$.


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Additional Information

William Heinzer
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907-1395
Email: heinzer@math.purdue.edu

Christel Rotthaus
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027
Email: rotthaus@math.msu.edu

Sylvia Wiegand
Affiliation: Department of Mathematics and Statistics, University of Nebraska, Lincoln, Nebraska 68588-0323
Email: swiegand@math.unl.edu

DOI: https://doi.org/10.1090/S0002-9939-00-05492-7
Keywords: Discrete rank-one valuation domain, \'{e}tale extension, excellent ring, Henselization, local uniformization, regular local domain
Received by editor(s): July 23, 1998
Received by editor(s) in revised form: March 22, 1999
Published electronically: July 27, 2000
Additional Notes: The authors thank the National Science Foundation and the National Security Agency for support for this research. In addition they are grateful for the hospitality and cooperation of Michigan State University, the University of Nebraska and Purdue University, where several work sessions on this research were conducted.
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 2000 American Mathematical Society

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